3
Solving problems with patterns
Discover Mathematics P5: Term 1, Unit 6, Lessons 5–7
GoalSolve real-life problems by writing a table, finding the rule and extending it to the answer.
New words
table · rows and columns used to organise numbersstart value · the amount at the beginning, before the rule is usedgrowth · how much something increases each step
Explanation
Many everyday problems follow a pattern. First find the start value, then find what changes each time. Write the first few terms in a table, say the rule in words, and extend the table to the question. Mariam has 20 LE and saves 15 LE every week. After 1 week she has 35 LE, after 2 weeks 50 LE, and so on. After 6 weeks she has 20 + 6 × 15 = 110 LE. If a quantity doubles each time, the rule is multiply by 2 and the numbers grow quickly: 1, 2, 4, 8, 16, 32.
| Week | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| Savings (LE) | 20 | 35 | 50 | 65 | 80 | 95 | 110 |
Worked examples
Mariam has 20 LE and saves 15 LE a week. After 6 weeks: 20 + 6 × 15 = 20 + 90 = 110 LE.
| Week | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Height (cm) | 4 | 6.5 | 9 | 11.5 | 14 |
| Day | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| Children | 1 | 2 | 4 | 8 | 16 | 32 |
Class activity
Pattern in my pocket. Choose something that grows by the same amount each week, like pocket money saved or pages read. Make a table for six weeks, write the rule in a sentence, and use it to predict week ten. Then check week ten by continuing the table.
Practice
1
A baker bakes 18 rolls in the first hour and then 12 rolls in every following hour. How many rolls has the baker baked in total after 5 hours?
18, 30, 42, 54, 66. After 5 hours, 66 rolls in all (18 + 4 × 12 = 66).
2
A cinema row 1 has 12 seats and each next row has 2 more seats. How many seats are in row 8?
12 + 7 × 2 = 12 + 14 = 26 seats.
3
On day 1 a video is shared with 3 people. Each day it is shared with 3 times as many people as the day before. How many people on day 4?
3, 9, 27, 81. On day 4, 81 people.
4
Karim has 35 LE and saves 12.5 LE a week. After how many weeks will he have 110 LE?
110 − 35 = 75 and 75 ÷ 12.5 = 6. After 6 weeks (35 + 6 × 12.5 = 110).
5
One ticket costs 6 LE, so n tickets cost 6 × n LE. How much do 9 tickets cost, and how many tickets can you buy for 72 LE?
9 tickets cost 6 × 9 = 54 LE. For 72 LE: 72 ÷ 6 = 12 tickets.